Quasi-normal modes of warped black holes and warped AdS/CFT correspondence

TL;DR

This work analytically determines the quasi-normal modes of scalar, vector, and spinor perturbations around spacelike stretched and null warped AdS3 black holes. By carefully accounting for local coordinate identifications that relate the black hole asymptotics to warped AdS3 spacetimes, the authors recast the QNM spectra in terms of warped AdS3 quantum numbers and show agreement with warped AdS/CFT predictions, including the extraction of conformal dimensions from isometries. The results provide strong evidence for the warped AdS/CFT correspondence and highlight subtleties in the dual dictionary, such as temperature normalization and the role of the U(1) momentum in determining operator dimensions. Potential extensions include gravitational perturbations and absorption cross sections to further corroborate the duality and its boundary structure.

Abstract

We analytically calculate the quasi-normal modes of various perturbations of spacelike stretched and null warped $AdS_3$ black holes. From AdS/CFT correspondence, these quasi-normal modes are expected to appear as the poles in momentum space of retarded Green functions of dual operators in CFT at finite temperature. We find that this is indeed the case, after taking into account of the subtle identification of quantum numbers. The subtlety comes from the fact that only after appropriate coordinate transformation the asymptotic geometries of warped black holes are the same as the ones of warped $AdS_3$ spacetimes. We show that in general the quasi-normal modes are in good agreement with the prediction of the warped AdS/CFT correspondence, up to a constant factor. As a byproduct, we compute the conformal dimensions of boundary operators dual to the perturbations. Our result gives strong support to the conjectured warped AdS/CFT correspondence.